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The European Physical Journal C

Entanglement dynamics for static two-level atoms in cosmic string spacetime

Pingyang He, Hongwei Yu, Jiawei Hu

Published Feb 1, 2020• 10 citations
Publisher

Abstract

Abstract We study the entanglement dynamics of two static atoms coupled with a bath of fluctuating scalar fields in vacuum in the cosmic string spacetime. Three different alignments of atoms, i.e. parallel, vertical, and symmetric alignments with respect to the cosmic string are considered. We focus on how entanglement degradation and generation are influenced by the cosmic string, and find that they are crucially dependent on the atom-string distance r, the interatomic separation L, and the parameter $$\nu $$ ν that characterizes the nontrivial topology of the cosmic string. For two atoms initially in a maximally entangled state, the destroyed entanglement can be revived when the atoms are aligned vertically to the string, which cannot happen in the Minkowski spacetime. When the symmetrically aligned two-atom system is initially in the antisymmetric state, the lifetime of entanglement can be significantly enhanced as $$\nu $$ ν increases. For two atoms which are initially in the excited state, when the interatomic separation is large compared to the transition wavelength, entanglement generation cannot happen in the Minkowski spacetime, while it can be achieved in the cosmic string spacetime when the position of the two atoms is appropriate with respect to the cosmic string and $$\nu $$ ν is large enough.

DOI
10.1140/epjc/s10052-020-7663-x

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Abstract We study the entanglement dynamics of two static atoms coupled with a bath of fluctuating scalar fields in vacuum in the cosmic string spacetime. Three different alignments of atoms, i.e. parallel, vertical, and symmetric alignments with respect to the cosmic string are considered. We focus on how entanglement degradation and generation are influenced by the cosmic string, and find that they are crucially dependent on the atom-string distance r, the interatomic separation L, and the parameter ν\nu ν ν that characterizes the nontrivial topology of the cosmic string. For two atoms initially in a maximally entangled state, the destroyed entanglement can be revived when the atoms are aligned vertically to the string, which cannot happen in the Minkowski spacetime. When the symmetrically aligned two-atom system is initially in the antisymmetric state, the lifetime of entanglement can be significantly enhanced as ν\nu ν ν increases. For two atoms which are initially in the excited state, when the interatomic separation is large compared to the transition wavelength, entanglement generation cannot happen in the Minkowski spacetime, while it can be achieved in the cosmic string spacetime when the position of the two atoms is appropriate with respect to the cosmic string and ν\nu ν ν is large enough.
We investigate the entanglement dynamics of two uniformly accelerated atoms with the same acceleration perpendicular to their separation. The two-atom system is treated as an open system coupled with fluctuating electromagnetic fields in the Minkowski vacuum, and in the Born--Markov approximation the master equation that describes the completely positive time evolution of the two-atom system is derived. In particular, we investigate the phenomena of entanglement degradation, generation, revival and enhancement. As opposed to the scalar-field case, the entanglement dynamics is crucially dependent on the polarization directions of the atoms. For the two-atom system with certain acceleration and separation, the polarization directions of the atoms may determine whether entanglement generation, revival or enhancement happens, while for entanglement degradation, they affect the decay rate of entanglement. A comparison between the entanglement evolution of accelerated atoms and that of static ones immersed in a thermal bath at the Unruh temperature shows that they are the same only when the acceleration is extremely small.
We study the entanglement dynamics for two uniformly accelerated two-level atoms in interaction with a bath of fluctuating electromagnetic fields in vacuum in the presence of a reflecting boundary. We consider two different alignments of atoms, i.e., parallel and vertical alignments with respect to the boundary. In particular, we focus on the effects of the boundary, and acceleration on the entanglement dynamics, which are closely related to the orientations of polarization. For the parallel case, the initial entanglement of two transversely polarizable atoms very close to the boundary can be preserved as if it were a closed system, while for two vertically polarizable atoms, the concurrence evolves two times as fast as that in the free space. In the presence of a boundary, entanglement revival is possible for two atoms initially in the symmetric state depending on the orientations of the atomic polarizations, which is in sharp contrast to the fact that the concurrence always decays monotonically in the free space. Interestingly, two initially separable atoms, for which entanglement generation can never happen in the free space with any given acceleration and separation, can get entangled in the presence of a boundary if they are aligned parallel to the boundary. The birth time of entanglement can be noticeably advanced or postponed for the parallel two-atom system placed close to the boundary, while the maximal concurrence during evolution can be significantly enhanced when the atoms are vertically aligned. Moreover, two inertial atoms with different polarizations remain separable all the time, while as the acceleration increases, the delayed birth of entanglement happens, and the nonzero concurrence can be enhanced.
We study, in the paradigm of open quantum systems, the entanglement dynamics of two uniformly accelerated atoms with the same acceleration perpendicular to the separation. The two-atom system is treated as an open system coupled with a bath of fluctuating massless scalar fields in the Minkowski vacuum, and the master equation that governs its evolution is derived. It has been found that, for accelerated atoms with a nonvanishing separation, entanglement sudden death is a general feature when the initial state is entangled, while for those in a separable initial state, entanglement sudden birth only happens for atoms with an appropriate interatomic separation and sufficiently small acceleration. Remarkably, accelerated atoms can get entangled in certain circumstances while the inertial ones in the Minkowski vacuum cannot. A comparison between the results of accelerated atoms and those of static ones in a thermal bath shows that uniformly accelerated atoms exhibit features distinct from those immersed in a thermal bath at the Unruh temperature in terms of entanglement dynamics.
A bstract We analyze the entanglement generation in a pair of qubits that experience the vacuum fluctuations of a scalar field in the Cosmic String spacetime. The qubits are modeled as Unruh-DeWitt detectors coupled to a massless scalar field. We introduce a Heisenberg XY -interaction between the qubits that enhances the generation of quantum correlations. It is supposed that the qubits begin at a general mixed state described by a density operator with no entanglement while the field stays at its vacuum state. In this way, we find the general properties and conditions to create entanglement between the qubits by exploiting the field vacuum fluctuations. We quantify the qubits entanglement using the Negativity measure based on the Peres-Horodecki positive partial transpose criterion. We find that the Cosmic String would increase the entanglement harvesting when both qubits are near the Cosmic String. When the qubits locations are far from the Cosmic String we recover the usual results for Minkowski space. The Heisenberg XY -interaction enhances the entanglement harvesting irrespective of the coupling nature (ferromagnetic or anti-ferromagnetic). When the qubits are far apart from each other we find a maximum entanglement harvesting at the resonance points between the Heisenberg coupling constant and the qubits energy gap.
We investigate the radiative processes of a quantum system composed by two identical two-level atoms in the de Sitter spacetime, interacting with a conformally coupled massless scalar field prepared in the de Sitter-invariant vacuum. We discuss the structure of the rate of variations of the atomic energy for two static atoms. Following a procedure developed by Dalibard, Dupont-Roc, and Cohen-Tannoudji, our intention is to identify in a quantitative way the contributions of vacuum fluctuations and the radiation reaction to the generation of quantum entanglement and to the degradation of entangled states. We find that when the distance between two atoms larger than the characteristic length scale, the rate of variation of atomic energy in the de Sitter-invariant vacuum behaves differently compared with that in the thermal Minkowski spacetime. In particular, the generation and degradation of quantum entanglement can be enhanced or inhibited, which are dependent not only on the specific entangled state but also on the distance between the atoms.
We study, in the framework of open quantum systems, the entanglement generation between two mutually independent static two-level atoms in de Sitter spacetime. We treat the two-atom system as an open system in interaction with a bath of fluctuating conformally coupled massless scalar fields in the de Sitter invariant vacuum and derive the master equation that governs its evolution. With the help of the partial transposition criterion, we analyze entanglement generation between the two initially separable atoms and find that static atoms in de Sitter spacetime exhibit distinct characteristics from those in a thermal bath in flat spacetime in terms of entanglement generation. So, in principle, one can tell whether he is in a thermal bath or in de Sitter space by checking the entanglement creation between two initially separable static atoms in certain circumstances.